Traditional tail covers are made in the form of a bag or other enclosure, and are attached to the animal by fastening a strap that extends over the back of the animal, and usually wraps around the neck of the animal. Such a tail cover is shown in the patent to Kingett et al., U.S. Pat. No. 5,062,256. Thus, traditional tail covers are difficult to install, and can irritate the animal on which they are installed.